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Tertiary Mathematics Education Mary Coupland, Peter K. Dunn, Linda Galligan, Greg Oates and Sven Trenholm

Abstract Mathematical and statistical education research relevant to students in tertiary settings is reviewed. This is an expanding field and is evolving as researchers shift their attention from the reporting of innovations in lecturing practice and course design to include a deeper consideration of the experiences of educators and learners in this space. The purposeful inclusion of group work and discussion, focus on concepts, authentic problem solving, interactions in lectures with student response systems and online learning are all changing the way mathematics and statistics are taught at this level. The authors note that traditional measures of achievement in the form of exam marks are still relied upon, and call for theory-based and theory-building research including investigations of depth of understanding, and of transfer of knowledge and skills to new situations. An emphasis on the learner’s experience and the employment of cross-disciplinary teams of researchers are further suggestions. Keywords Undergraduate mathematics and statistics education ogy in learning mathematics and statistics


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M. Coupland (&) University of Technology Sydney, Broadway, Australia e-mail: [email protected] P.K. Dunn University of the Sunshine Coast, Maroochydore, Australia e-mail: [email protected] L. Galligan University of Southern Queensland, Toowoomba, Australia e-mail: [email protected] G. Oates University of Tasmania, Launceston, Australia e-mail: [email protected] S. Trenholm University of South Australia, Adelaide, Australia e-mail: [email protected] © Springer Science+Business Media Singapore 2016 K. Makar et al. (eds.), Research in Mathematics Education in Australasia 2012–2015, DOI 10.1007/978-981-10-1419-2_10

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1 Introduction This chapter surveys the growing field of research into mathematics learning and teaching at the tertiary level. Significantly, the Australian Mathematical Society established in 2015 a Special Interest Group in Mathematics Education (SIGME) which has among its goals the promotion of inquiry and discussion about tertiary mathematics education. This interest is worldwide: 2015 sees the first issue of a new journal, the International Journal of Research in Undergraduate Mathematics Education, with six Australasians on the Editorial Board. In addition, 2016 will see the launch of a new international conference series with INDRUM 2016, the first conference of the International Network for Didactic Research in University Mathematics. The four-yearly International Congress on Mathematical Education (ICME) series continues to include a Topic Study Group on mathematics education at tertiary level, and in 2012 at ICME there was also a report of a Survey Team on Key Mathematical Concepts in the Transition from Secondary School to University. Against this background, we located relevant reports by searching journals and refereed